Jane Evans receives payments of$$ $$900$ at the beginning of each month from a pension fund of $$$$72$ comma $50072,500.$ Interest earned by the fund is$6\mathrm{.}3\%$ compounded monthly.

$($a$)$ What is the number of payments Jane will$$ receive?

$($b$)$ What is the size of the final$$ payment?

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Part $1$

$($a$)$ The number of payments Jane will receive is

$$

enter your response here.

$($Round up to the nearest whole$$ number.$)$

Part $2$

$($b$)$ The amount of the final payment is $$$

$$

enter your response here.

$($Round to the nearest cent as$$ needed.$)$